A semiclassical description of diffusive spin transport in spin valves, which takes into account the transverse components of spin accumulation, is used to calculate the second harmonic voltage response to a low-frequency current. The description is applied to single as well as dual spin valves, with the magnetic moment of the sensing layer slightly tilted out of the equilibrium position by an in-plane external magnetic field. In the case of double spin valves, only the antiparallel configuration is considered since the spin torque in this configuration is enhanced, while in the parallel configuration it is significantly reduced. In both cases considered, the second harmonic voltage response and the relevant magnetoresistance are shown to be significantly dependent on the transverse spin penetration length.

1.
N. M.
Baibich
,
J. M.
Broto
,
A.
Fert
,
F.
Nguyen Van Dau
,
F.
Petroff
,
P.
Eitenne
,
G.
Creuzer
,
A.
Friederich
, and
J.
Chazelas
,
Phys. Rev. Lett.
61
,
2472
(
1988
).
2.
G.
Binasch
,
P.
Grunberg
,
F.
Saurenbach
, and
W.
Zinn
,
Phys. Rev. B
39
,
4828
(
1989
).
3.
R. E.
Camley
and
J.
Barnaś
,
Phys. Rev. Lett.
63
,
664
(
1989
).
4.
T.
Valet
and
A.
Fert
,
Phys. Rev. B
48
,
7099
(
1993
).
5.
A.
Fert
and
I. A.
Campbell
,
Phys. Rev. Lett.
21
,
1190
(
1968
).
6.
M. A.
Gijs
and
G. E.
Bauer
,
Adv. Phys.
46
,
285
(
1997
).
7.
J.
Bass
and
W. P.
Pratt
, Jr.
,
J. Phys.: Condens. Matter
19
,
183201
(
2007
).
8.
J. C.
Slonczewski
,
J. Magn. Magn. Mater.
159
,
L1
(
1996
).
9.
10.
J.
Slonczewski
,
J. Magn. Magn. Mater.
247
,
324
(
2002
).
11.
M. D.
Stiles
and
A.
Zangwill
,
Phys. Rev. B
66
,
014407
(
2002
).
12.
A.
Brataas
,
G. E.
Bauer
, and
P. J.
Kelly
,
Phys. Rep.
427
,
157
(
2006
).
13.
J.
Barnaś
,
A.
Fert
,
M.
Gmitra
,
I.
Weymann
, and
V. K.
Dugaev
,
Phys. Rev. B
72
,
024426
(
2005
).
14.
M.
Zwierzycki
,
P. A.
Khomyakov
,
A. A.
Starikov
,
K.
Xia
,
M.
Talanana
,
P. X.
Xu
,
V. M.
Karpan
,
I.
Marushchenko
,
I.
Turek
,
G. E. W.
Bauer
,
G.
Brocks
, and
P. J.
Kelly
,
Phys. Status Solidi B
245
,
623
(
2008
).
15.
M.
Zwierzycki
,
Y.
Tserkovnyak
,
P. J.
Kelly
,
A.
Brataas
, and
G. E. W.
Bauer
,
Phys. Rev. B
71
,
064420
(
2005
).
16.
A.
Shpiro
,
P. M.
Levy
, and
S.
Zhang
,
Phys. Rev. B
67
,
104430
(
2003
).
17.
J.
Zhang
,
P. M.
Levy
,
S.
Zhang
, and
V.
Antropov
,
Phys. Rev. Lett.
93
,
256602
(
2004
).
18.
A. A.
Kovalev
,
G. E. W.
Bauer
, and
A.
Brataas
,
Phys. Rev. B
73
,
054407
(
2006
).
19.
C.
Petitjean
,
D.
Luc
, and
X.
Waintal
,
Phys. Rev. Lett.
109
,
117204
(
2012
).
20.
A.
Ghosh
,
S.
Auffret
,
U.
Ebels
, and
W. E.
Bailey
,
Phys. Rev. Lett.
109
,
127202
(
2012
).
21.
Y.
Tserkovnyak
,
A.
Brataas
,
G. E. W.
Bauer
, and
B. I.
Halperin
,
Rev. Mod. Phys.
77
,
1375
(
2005
).
22.
T.
Taniguchi
,
S.
Yakata
,
H.
Imamura
, and
Y.
Ando
,
IEEE Trans. Magn.
44
,
2636
(
2008
).
23.
T.
Taniguchi
,
S.
Yakata
,
H.
Imamura
, and
Y.
Ando
,
Appl. Phys. Express
1
,
031302
(
2008
).
24.
H.
Yu
,
J.
Dubois
,
S.
Granville
,
D. P.
Yu
, and
J.-P.
Ansermet
,
J. Phys. D: Appl. Phys.
42
,
175004
(
2009
).
25.
J.
Dubois
and
J.-P.
Ansermet
,
Phys. Rev. B
78
,
184430
(
2008
).
26.
A. A.
Kovalev
,
G. E. W.
Bauer
, and
A.
Brataas
,
Phys. Rev. B
75
,
014430
(
2007
).
27.
M.
Gmitra
and
J.
Barnaś
, in
Toward Functional Nanomaterials
, edited by
Z.
Wang
(
Springer
,
2009
), pp.
285
322
.
28.
A.
Brataas
,
Yu. V.
Nazarov
, and
G. E. W.
Bauer
,
Eur. Phys. J. B
22
,
99
(
2001
).
29.
Y. B.
Bazaliy
,
B. A.
Jones
, and
S.-C.
Zhang
,
Phys. Rev. B
69
,
094421
(
2004
).
30.
L.
Berger
,
J. Appl. Phys.
93
,
7693
(
2003
).
31.
P.
Baláž
,
M.
Gmitra
, and
J.
Barnaś
,
Phys. Rev. B
80
,
174404
(
2009
).
32.
A. J.
Newell
,
W.
Williams
, and
D. J.
Dunlop
,
J. Geophys. Res.
98
,
9551
, doi: (
1993
).
33.
B. S.
Chun
,
C.
Fowley
,
M.
Abid
, and
J. M. D.
Coey
,
J. Phys. D: Appl. Phys.
43
,
025002
(
2009
).
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